A new realization criterion for 2-D digital filters in the Fornasini–Marchesini second model with interference

•A new criterion for H∞H∞ stability of 2-D digital filters in Fornasini–Marchesini second model is proposed.•The effect of external interference on 2-D filters can be reduced to an attenuation level.•The criterion guarantees asymptotic stability without external interference.•The criterion is described by linear matrix inequality.

Stability criteria have been proposed previously by Ahn for two-dimensional (2-D) digital filters described by the Roesser model with external interference. However, no stability criteria have yet been established for 2-D digital filters described by the Fornasini–Marchesini second model. In this paper, we propose a new realization criterion for 2-D digital filters in the Fornasini–Marchesini second model with saturation arithmetic and external interference. This new criterion guarantees that 2-D digital filters in this model are asymptotically stable with a guaranteed H∞H∞ performance. The criterion is described by linear matrix inequalities (LMIs). Illustrative examples show the effectiveness of the proposed new criterion.